Is my girl in QT broody?

Hey folks! I have a lone BR lady (Nelly) in QT. Long story short - she was supposed to be eaten. She's 3 years old. I decided that we were not going to eat her, but she was new to our farm, so I put her in QT. She's in the front yard, away from our other chickens and will remain there until her month time is up to make sure she's not harboring any parasite or illness that I can see. She's a sweet girl. I am going to be setting up a fence for her so that she has more room, but it seems that she doesn't want to leave her makeshift nest. She's not mean or in a "trance." She comes out to eat and drink and goes back in. I can lure her out with a strawberry. She's very vocal. We've had her now a little over a week. I didn't think she'd lay an egg right away, but I found one in there today. I didn't remove it because as soon as she finished eating, she went back in. I know she's been with a rooster - what breed, who knows. The farmer has many types; mainly Polish and Araucana. I'm kind of curious to see what would hatch.

Sooo.... do I leave the egg in there? Even if she isn't broody, will she hatch the egg by default, being that she likes to sit in there so often?

Thanks for your answers. As you can tell - I'm new to this aspect of chicken keeping.

She does look a bit stinky in that second photo!!! I knew she was a BR, silly.

Thanks for your help/opinion. I'll leave her with the egg and see what happens. I hope she doesn't crack it. Hmm. Even if she doesn't "sit" on it persay, but moves it around every so often when she goes in and out of there... it may still hatch, right? It's warm outside....

Well so much for that egg!! Some sort of predator wanted in last night and started to tear her cages apart. There were feathers everywhere! The egg was smashed in the process. A small hole was also beside the cage. I'm going to have to make sure the poor girl is safer. I was surprised she wasn't injured after seeing all those feathers everywhere.